Nonlinear Diffusion Method Research Articles

Enhanced Infrared Detection Algorithm for Weak Targets in Complex Backgrounds

In this article, we design a new lightweight infrared optical system that fully meets airborne settings and greatly reduces the collection of invalid information. This new system targets the technical problems of stray light, strong invalid information, weak texture information of small targets, and low intensity of valid information under a complex background, which lead to difficult identification of small targets. Image enhancement of weak, small targets against complex backgrounds has been the key to improving small-target search and tracking technology. For the complex information that is still collected, an improved two-channel image enhancement processing algorithm is proposed: the A-channel adopts an improved nonlinear diffusion method and improved curvature filtering, and the B-channel adopts bootstrap filtering and a local contrast enhancement algorithm. The weak target is then extracted by the algorithm of weighted superposition. The false alarm rate is effectively weakened, and robustness is improved. As a result of the experimental data analysis, the method can effectively extract the weak targets in complex backgrounds, such as artificial backgrounds, surface vegetation, etc., enlarge the target gray value, and reduce Fa by 56%, compared with other advanced methods, while increasing Pd by 17%. The algorithm proposed in this paper is of great significance and value for weak target identification and tracking, and it has been successfully applied to industrial detection, medical detection, and in the military field.

Method for seismic signal denoising based on generalized S-transform and nonlinear complex diffusion

This paper aims to improve the problem of seismic signal enhancement and noise filtering by utilizing the generalized S-transform (GST) and nonlinear complex diffusion (NCD) methods. GST and its inverse transform (IGST) can decompose the original seismic signal into several sub-component signals in terms of the instantaneous frequencies to discern the distribution of various frequencies in the entire signal. The imaginary value generated by the NCD process, which can be used as the directional structure indicator to suppress the noise and enhance the effective signal. Therefore, we present a denoise method of seismic signal based on generalized S-transform and nonlinear complex diffusion (GSNCD). GSNCD, is a decomposition, denoise, and reconstruction method, with three key features: (1) A new GST transform is proposed under the GST framework, which uses the characteristic of the higher frequency resolution in high frequency and the higher time resolution in low frequency to decompose the signal into sub-component signals as different frequencies, and the sub-component signals are used to determine the structural tensor of seismic signal; (2) a fixed diffusion coefficient of complex diffusion is improved to adjust the adaptive iteration step size; (3) the sub-component seismic signals are calculated to avoid filtering deviation caused by fixed inclination angle. Finally, we reconstruct the processed sub-component signals into a complete signal. The simulations and real example fully verify the effectiveness of GSNCD in seismic signal denoising, with particular improvements in the attenuation at the data edge. In the ground motion signal test, the signal-to-noise ratio (SNR) after denoising by GSNCD increased from −2.50 dB to 13.83 dB. In two scenarios tests of exploration signals, the SNR of GSNCD is 12.09 dB and 11.19 dB, respectively, demonstrating better relative error and stability compared to other denoise methods such as Wavelet, empirical mode decomposition (EMD), adaptive NCD (ANCD), damped rank-reduction (DRR) and structural filtering method applied in the low-SNR seismic signal.

Nonlinear computer image scene and target information extraction based on big data technology

Abstract To explore the extraction of computer image scene and target information, a nonlinear method based on big data technology is proposed. The method can decompose the computer image into a plurality of components when the SAR computer image is processed such as target extraction and computer image compression, which represent different captured image features, respectively. Selecting the most suitable processing method according to the characteristics of different components can greatly improve the performance. Using nonlinear diffusion method, the computer image is decomposed into structural components representing large-scale structural information and texture components representing small-scale detailed information, and the automatic threshold estimation in the diffusion process is studied. The LAIDA criterion is introduced into the automatic threshold solution of nonlinear diffusion-based computer image decomposition to test and evaluate the diffusion process of various diffusion parameter forms. The results show that the experimental outcome of the diffusion decomposition based on automatic threshold estimation is very close on each index, which shows that using automatic threshold estimation, no matter what diffusion index is used, very close results can be obtained. Specifically, for each algorithm, the parameter estimation threshold l for outliers plays an obvious role. The third is the degree of initiative of the estimation process. The larger the L, the larger the outlier, which will lead to a greater extent of the diffusion process, resulting in a continuous decrease in the structural similarity index and compositional correlation. It is proved that the algorithm has strong global search ability, can effectively avoid premature convergence, has fast convergence speed, and good long stability. It can be widely used for optimization of various multimodal functions.

Visual Communication Effect Modeling of Public Service Advertisements Based on Fractional Differential Equations

Abstract This paper establishes the visual communication effect model of public service advertisement based on a fractional differential equation. In this paper, a guided filter is used to smooth the image and improve the grayscale phenomenon of the image. Then this paper adopts a method based on wavelet transform to obtain the reference line of the target point source. This achieves the suppression of the background baseline of the target point. Finally, this paper extracts the edge detail feature value in the public service billboard, which realizes the fusion recognition of the missing part in the advertising image. Then this paper transforms it into the problem of separating the object's foreground from the image's background. Finally, this paper uses an improved nonlinear diffusion method to suppress the tiny image detail signal. Experiments show that the algorithm has good optical transmission performance and is not limited by the size of public service advertisement images.

Recasted nonlinear complex diffusion method for removal of Rician noise from breast MRI images

The evolution of magnetic resonance imaging (MRI) leads to the study of the internal anatomy of the breast. It maps the physical features along with functional characteristics of selected regions. However, its mapping accuracy is affected by the presence of Rician noise. This noise limits the qualitative and quantitative measures of breast image. This paper proposes recasted nonlinear complex diffusion filter for sharpening the details and removal of Rician noise. It follows maximum likelihood estimation along with optimal parameter selection of complex diffusion where the overall functionality is balanced by regularization parameters. To make recasted nonlinear complex diffusion, the edge threshold constraint “k” of diffusion coefficient is reformed. It is replaced by the standard deviation of the image. It offers a wide range of threshold as variability present in the image with respect to edge. It also provides an automatic selection of “k” instead of user-based value. A series of evaluation has been conducted with respect to different noise ratios further quality improvement of MRI. The qualitative and quantitative assessments of evaluations are tested for the Reference Image Database to Evaluate Therapy Response (RIDER) Breast database. The proposed method is also compared with other existing methods. The quantitative assessment includes the parameters of the full-reference image, human visual system, and no-reference image. It is observed that the proposed method is capable of preserving edges, sharpening the details, and removal of Rician noise.

Convergence analysis of a new dynamic diffusion method

This paper presents the numerical analysis for a variant of the nonlinear multiscale Dynamic Diffusion (DD) method for the advection-diffusion-reaction equation initially proposed by Arruda et al. [1] and recently studied by Valli et al. [2]. The new DD method, based on a two-scale approach, introduces locally and dynamically an extra stability through a nonlinear operator acting in all scales of the discretization. We prove existence of discrete solutions, stability, and a priori error estimates. We theoretically show that the new DD method has convergence rate of O(h1/2) in the energy norm, and numerical experiments have led to optimal convergence rates in the L2(Ω), H1(Ω), and energy norms.

Seismic Signal Enhancement and Noise Suppression Using Structure-Adaptive Nonlinear Complex Diffusion

In seismic exploration, effective seismic noise attenuation along with seismic signal preservation is a key problem for seismic signal processing. The seismic data acquired from complex environments usually have a low signal-to-noise ratio (SNR) and nonstationary random noise that makes it difficult to accurately restore seismic signals. For enhancing seismic signals and filtering nonstationary random noise, we propose a structure-adaptive nonlinear complex diffusion method (ANCD) based on the regularized complex shock diffusion (CSD) by exploiting the structure-adaptive diffusion coefficients. The proposed complex diffusion method makes use of the imaginary value which is generated by a complex diffusion process as a directional structure indicator to guide the diffusion coefficients, by cooperating with spatially variant structure factors associated with the eigenvalues and eigenvectors of the structure tensor. In this way, the structural-adaptive diffusion term of ANCD allows the diffusion process along seismic structures, and the resulting imaginary part in turn enables the shock term to enhance the seismic signals with steep dips and rapidly varying slopes. The proposed method is tested on the synthetic seismic data and field seismic data acquired from the forest belt and desert area. The results show that the ANCD achieves a superior tradeoff between suppressing complicated random noise and preserving the seismic structures compared with the state-of-the-art seismic denoising methods.

Texture classification using optimized local ternary patterns with nonlinear diffusion as pre-processing

The main focus of this paper is to improve the performance of the texture model Optimized Local Ternary Patterns (OLTP), which is known as one of the successful variants of the texture model Local Binary Patterns (LBP), a well known method for texture analysis and its applications. Generally preprocessing is used in digital image processing for reducing the unwanted noise and disturbances in such a way that it improves the quality of the image. Preprocessing not only removes the distortions but also enhances the features of the image for further processing. To achieve better recognition accuracy, the texture model OLTP was combined with a preprocessing method that uses nonlinear diffusion method as a preprocessing tool in this paper, with the hope that this idea will surely improve the local feature description and texture classification process. This nonlinear diffusion method uses two newly developed edge stopping functions for preprocessing. This proposed method is tested with two standard texture datasets namely Brodatz Dataset and Usptex dataset. The results show that the use of the preprocessing step really improved the texture classification accuracy.

An automatic stopping criterion for nonlinear anisotropic diffusion

Nonlinear anisotropic diffusion (NAD) filtering is a procedure based on nonlinear evolution PDEs which seeks to improve images qualitatively by removing noise while preserving details and even enhancing edges. However, well-known implementations are sensitive to parameters which are necessarily tuned to sharpen a narrow range of edge slopes; otherwise, edges are either blurred or staircased [Kee2002]. One important parameter is the iterations number, for that reason, in this paper a stopping criterion to halt the diffusion process is proposed. To meet this goal, two stopping criteria were compared. The first is the stopping criterion proposed by Joao et. al. [Joa2016], which is based on the Mean Squared Error (MSE). The second is our proposed method based on the CIRR contrast measure. To this end, a comparative analysis of five diffusion methods is performed. Four of them are nonlinear anisotropic diffusion methods and the fifth is the Perona-Malik method. According to the tests performed, the number of iterations required by the smoothing algorithms using the proposed stopping criterion is lower.

Using performance reference compounds to compare mass transfer calibration methodologies in passive samplers deployed in the water column.

Performance reference compounds (PRCs) are often added to passive samplers prior to field deployments to provide information about mass transfer kinetics between the sampled environment and the passive sampler. Their popularity has resulted in different methods of varying complexity to estimate mass transfer and better estimate freely dissolved concentrations (Cfree ) of targeted compounds. Three methods for describing a mass transfer model are commonly used: a first-order kinetic method, a nonlinear least squares fitting of sampling rate, and a diffusion method. Low-density polyethylene strips loaded with PRCs and of 4 different thicknesses were used as passive samplers to create an array of PRC results to assess the comparability and reproducibility of each of the methods. Samplers were deployed in the water column at 3 stations in New Bedford Harbor (MA, USA). Collected data allowed Cfree comparisons to be performed in 2 ways: 1) comparison of Cfree derived from one thickness using different methods, and 2) comparison of Cfree derived by the same method using different thicknesses of polyethylene. Overall, the nonlinear least squares and diffusion methods demonstrated the most precise results for all the PCBs measured and generated Cfree values that were often statistically indistinguishable. Relative standard deviations (RSDs) for total PCB measurements using the same thickness and varying model types ranged from 0.04 to 12% and increased with sampler thickness, and RSDs for estimates using the same method and varying thickness ranged from 8 to 18%. Environmental scientists and managers are encouraged to use these methods when estimating Cfree from passive sampling and PRC data. Environ Toxicol Chem 2018;37:2089-2097. Published 2018 Wiley Periodicals Inc. on behalf of SETAC. This article is a US government work and, as such, is in the public domain in the United States of America.

TomoEED: fast edge-enhancing denoising of tomographic volumes.

TomoEED is an optimized software tool for fast feature-preserving noise filtering of large 3D tomographic volumes on CPUs and GPUs. The tool is based on the anisotropic nonlinear diffusion method. It has been developed with special emphasis in the reduction of the computational demands by using different strategies, from the algorithmic to the high performance computing perspectives. TomoEED manages to filter large volumes in a matter of minutes in standard computers. TomoEED has been developed in C. It is available for Linux platforms at http://www.cnb.csic.es/%7ejjfernandez/tomoeed. Supplementary data are available at Bioinformatics online.

Image despeckling and deblurring via regularized complex diffusion

In this paper an image restoration and enhancement model is being proposed, which is suitable for multiplicative data-dependent speckle noise (whose intensity is Gamma distributed) under linear shift-invariant blurring artifacts. The proposed strategy devises a nonlinear second-order diffusive-reactive model for enhancing and restoring images degraded by the aforementioned scenario. The reactive term is derived based on the Maximum a posteriori (MAP) estimator, to make it adaptive to the noise distribution in the input data. This noise-adaptive reactive term helps to restore and enhance the images under data-correlated noise setup. Unlike the other second-order nonlinear diffusion methods, the proposed solution preserves edges and details and reduces piecewise constant approximation in the homogeneous intensity regions in the course of its evolution. The experimental results demonstrated in this paper duly support the above claims.

PolSAR anisotropic diffusion filter with a refined similarity measure and an adaptive fidelity constraint

ABSTRACTThe presence of speckle complicates the tasks of interpreting and analysing polarimetric synthetic aperture radar (PolSAR) images. The nonlinear anisotropic diffusion (AD) method has been found to perform well in removing image noise. In this article, we propose a new AD method for PolSAR speckle reduction. An iterative refinement method is employed to measure the similarity between pixels and construct the diffusion coefficient in the iteration process, by considering both information in the original speckled image and the restored image of the last iteration. In addition, to alleviate the over-smoothing problem the conventional AD methods often encounter, an adaptive fidelity constraint is added into the diffusion equation by considering local heterogeneity information and the amount of noise. Experiments on both simulated and real PolSAR images confirm the ability of the proposed method to both suppress speckle and retain image details.

Image decomposition-based structural similarity index for image quality assessment

Perceptual image quality assessment (IQA) adopts a computational model to assess the image quality in a fashion, which is consistent with human visual system (HVS). From the view of HVS, different image regions have different importance. Based on this fact, we propose a simple and effective method based on the image decomposition for image quality assessment. In our method, we first divide an image into two components: edge component and texture component. To separate edge and texture components, we use the TV flow-based nonlinear diffusion method rather than the classic TV regularization methods, for highly effective computing. Different from the existing content-based IQA methods, we realize different methods on different components to compute image quality. More specifically, the luminance and contrast similarity are computed in texture component, while the structural similarity is computed in edge component. After obtaining the local quality map, we use texture component again as a weight function to derive a single quality score. Experimental results on five datasets show that, compared with previous approaches in the literatures, the proposed method is more efficient and delivers higher prediction accuracy.

Volume preserving mesh parameterization based on optimal mass transportation

In order to convert a finite element mesh model to the spline representation for the purpose of isogeometric analysis, one needs to parameterize the solid. This work introduces a novel volumetric parameterization method, which guarantees to be free of volume distortion.Given a simply connected tetrahedral mesh with a single boundary surface, we first compute a harmonic map from the boundary triangle mesh to the unit sphere by non-linear heat diffusion method; then we use the surface harmonic map as the boundary condition to compute the volumetric harmonic map to parameterize the solid onto the unit solid ball; finally we compute an optimal mass transportation map from the unit solid ball with the push-forward volume element induced by the harmonic map onto itself with the Euclidean volume element. The composition of the volumetric harmonic map and the optimal mass transportation map gives an volume-preserving parameterization.The method has solid theoretic foundation, and is based on conventional algorithms in computational geometry, easy to implement. We have thoroughly tested our algorithm on many solid models in reality. The experimental results demonstrate the efficiency and efficacy of the proposed method. To the best of our knowledge, it is the first work addressing volume-preserving parameterization in the literature.

Hyperbolic Harmonic Mapping for Surface Registration.

Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints. This work conquers this problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints. The computational algorithms are based on Ricci flow and nonlinear heat diffusion methods. The approach is general and robust. We employ our algorithm to study the constrained surface registration problem which applies to both computer vision and medical imaging applications. Experimental results demonstrate that, by changing the Riemannian metric, the registrations are always diffeomorphic and achieve relatively high performance when evaluated with some popular surface registration evaluation standards.

Motion deblurring using normalized nonlinear diffusion regularization

Motion deblurring is a hard and hot topic which has been made significant progress in the last decade. It is hard because it is an ill-posed problem for both kernel and latent image estimation. In this paper, we use normalized nonlinear diffusion regularization for motion deblurring. By using nonlinear diffusion method, our method can deal with edges adaptively. Normalized nonlinear diffusion term can make the energy decreasing while in the solving process and the minimum of the cost function is the real solution. Because the result derived from the energy function give the lowest cost, our method does not need any auxiliary method for solving the energy function besides multiscale implementation. Using the estimated kernel, the final clear image can be got by total variation method. Experiments demonstrate the validity of the proposed method.

Performance Evaluations of Image Denoising System based on Nonlinear Diffusion Method in Wavelet Domain

Image processing is always being a research field for the researcher. The Image denoising is one of the important areas of image processing. There are several methods for image denoising in spatial and transform domain. The current trends of the image denoising research are the evolution of mixed domain methods. In this paper, a mixed domain image denoising method is proposed, which is based on the wavelet transform, median filter and nonlinear diffusion. The wavelet transform is used in this paper to convert the spatial domain image to wavelet domain coefficients. The detail component are removed due to the most of the image part is in approximation part. The approximation coefficient is then filtering by nonlinear diffusion and median filter separately. The peak signal to noise ratio (PSNR), root mean square error (RMSE) and mean structural similarity index matrix (MSSIM) are used as the performance parameter. The different wavelet families are used to optimize the performance of denoising. The Coiflet2 wavelet and diffusion algorithm are giving the best denoising result.

Application of nonlinear nodal diffusion method for a small research reactor

Nodal diffusion methods are usually used for LWR calculations and rarely used for research reactor calculations. A unified nodal method with an implementation of the coarse mesh finite difference acceleration was developed for use in plate type research reactor calculations. It was validated for two PWR benchmark problems and then applied for IAEA MTR benchmark problem for static calculations to check the validity and accuracy of the method. This work was conducted to investigate the unified nodal method capability to treat material testing reactor cores. A 10MW research reactor core is considered with three calculation cases for low enriched uranium fuel depending on the core burnup status of fresh, beginning-of-life, and end-of-life cores. The validation work included criticality calculations, flux distribution, and power distribution; in addition, a comparison between different fuel materials with the same uranium content was conducted. The homogenized two-group cross sections were generated using the TRITON–NEWT system. The results were compared with a reference, which was taken from IAEA-TECDOC-233. The unified nodal method provides satisfactory results for an all-rod out case, and the three-dimensional, two-group diffusion model can be considered accurate enough for MTR core calculations.

Nonlinear Diffusion based on Bayesian Estimator in Laplacian Pyramid Domain for Ultrasonic Speckle Reduction

Laplacian pyramid based nonlinear diffusion (LPND) method is proposed for speckle noise reduction in medical ultrasound imaging. In this method, speckle is removed by nonlinear diffusion filtering of bandpass ultrasound images in Laplacian pyramid domain. For nonlinear diffusion in each pyramid layer, a Bayesian threshold is automatically determined by a variation of robust median estimator. The proposed LPND method reduces speckle noise significantly while preserving sharp image details. The superiority of the proposed LPND over the conventional LPND based on Gaussian filtering and LPND method based on Butterworth filtering based speckle reduction technique is demonstrated by applying them on synthetic and real ultrasound B-mode images.